In the Lands of Conflict: Age of Kings mod, each player control a Capital Building (Castle). The Castle is center for many events such as Gate Control, Hero (King) resurrection, tax rate, and used to declare war or make alliances with other players.

Once a Castle is destroyed, the only remaining objective for other players, is to kill the Queen to defeat the player and gain control of his units and settlements.

My question to you is, should players be able to capture a Neutral Capital Buildings i.e. gain a second chance?

Intriguing.
Perhaps players should be able to capture eachother's castles as well? That way it will have some sort of a "conquest" feeling to it, I don't know if that's what you're going for though.
Neutral castles shouldn't be much better than regular castles though, or else it might just turn into some kind of a 'I have a neutral castle thus I win' thing. Which I assume is not good.

Intriguing.
Perhaps players should be able to capture eachother's castles as well? That way it will have some sort of a "conquest" feeling to it, I don't know if that's what you're going for though.
Neutral castles shouldn't be much better than regular castles though, or else it might just turn into some kind of a 'I have a neutral castle thus I win' thing. Which I assume is not good.

Players ARE able to capture another player's Castle.

Well, I figured that since there's only 2 Neutral Castles, it should be harder to take & easier to defend compared to other settlements. Not to mention, that the player gain an additional Castle, which is huge.

While the castle you showed is a WIP, it seems extremely easy to defend. The concept of spiralling up before reaching the front gates mean more ranged units will be attack for a long time before being under attack by melee siege units, but maybe that's what you intend (?). I guess if it is very difficult to take from the beginning and therefore the player must take a risk to try and conquest it then it is understandable.

EDIT: Well I haven't really seen much of other castles so I don't know how this one compares in terms of difficulty to defend, but I just wanted to point out it looks pretty easy to hold off against intruders for such an important building.